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Cold atoms bring new opportunities to study quantum magnetism, and inparticular, to simulate quantum magnets with symmetry greater than $SU(2)$.Here we explore the topological excitations which arise in a model of coldatoms on the triangular lattice with $SU(3)$ symmetry. Using a combination ofhomotopy analysis and analytic field-theory we identify a new family ofsolitonic wave functions characterised by integer charge ${\bf Q} = (Q_A, Q_B,Q_C)$, with $Q_A + Q_B + Q_C = 0$. We use a numerical approach, based on avariational wave function, to explore the stability of these solitons on afinite lattice. We find that, while solitons with charge ${\bf Q} = (Q, -Q, 0)$are stable, wave functions with more general charge spontaneously decay intopairs of solitons with emergent interactions. This result suggests that itcould be possible to realise a new class of interacting soliton, with noclassical analogue, using cold atoms. It also suggests the possibility of a newform of quantum spin liquid, with gauge--group U(1)$\times$U(1).

Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice